Theorem simp3i 1141

Description: Infer a conjunct from a triple conjunction. (Contributed by NM, 19-Apr-2005.)

Hypothesis

Ref	Expression
3simp1i.1	⊢ (𝜑 ∧ 𝜓 ∧ 𝜒)

Assertion

Ref	Expression
simp3i	⊢ 𝜒

Proof of Theorem simp3i

Step	Hyp	Ref	Expression
1		3simp1i.1	. 2 ⊢ (𝜑 ∧ 𝜓 ∧ 𝜒)
2		simp3 1138	. 2 ⊢ ((𝜑 ∧ 𝜓 ∧ 𝜒) → 𝜒)
3	1, 2	ax-mp 5	1 ⊢ 𝜒

Syntax hints:   ∧ w3a 1086

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8

This theorem depends on definitions:  df-bi 207  df-an 396  df-3an 1088

This theorem is referenced by:  hartogslem2  9448  harwdom  9496  divalglem6  16325  structfn  17083  strleun  17084  oppchomfval  17637  sratset  21135  srads  21137  tngip  24591  dfrelog  26530  log2ub  26915  birthdaylem3  26919  birthday  26920  divsqrtsum2  26949  harmonicbnd2  26971  lgslem4  27267  lgscllem  27271  lgsdir2lem2  27293  lgsdir2lem3  27294  mulog2sumlem1  27501  siilem2  30927  h2hva  31049  h2hsm  31050  h2hnm  31051  elunop2  32088  wallispilem3  46311  wallispilem4  46312  prstchomval  49804  cnelsubclem  49848